If I Only Had a Brain…
If I Only Had a Brain…
The Wizard of Oz — MGM (1939) — Harold Arlen & E.Y. “Yip” Harburg
“I could while away the hours, conferrin’ with the flowers, consultin’ with the rain…” — or maybe just find the vertex of a parabola.
“If I Only Had a Vertex” — the quadratic parody this song inspired
This is the whole point of the page. The Scarecrow’s longing for a brain, set to one of the most singable melodies in film history, turned out to be the perfect vehicle for a math parody. The quadratic function y = ax² + bx + c has a vertex to be found. The Scarecrow wants a brain. The fit was too good to leave alone. TNT used this parody as a classroom tool for years before it found its permanent home here. Get a class to sing “But I sure need a vertex!” in unison and they tend to remember what a vertex is.
“If I Only Had a Vertex”
y = f(x) = ax2 + bx + c
But functions when Quadratic
Don’t give me a Complex…
I can hardly keep from laugh-n when parabolas I’m a-graphin’
But I sure need a vertex!
I can classify that puppy
I look at ‘a’ and check:
And I really start a-rolling cuz
I know ‘a’ is shape-control’n
But I sure need a vertex!
where down-ies reach their high…
The vertex as you know,
is the place, where up-ies ‘low.’
When it’s vertically-a-shifted
Due to the ‘c’s effects…
And my mind is accept’n
That the ‘c’s a y-intercept’n
But I sure need a vertex!
If I knew their top from bottom
I would not feel so vexed
I could use h = −b / (2a)
Plug it in and get a k
I’d know that dumb vertex!
©1997 TTG
About the song — “If I Only Had a Brain” by Harold Arlen & E.Y. Harburg
Written by Harold Arlen (music) and Edgar Yipsel “Yip” Harburg (lyrics), “If I Only Had a Brain” premiered on-screen on August 15, 1939. It is the first of three parallel “wish songs” in the film, each built on the same melodic frame. The Tin Man wants “If I Only Had a Heart”; the Cowardly Lion wants “If I Only Had the Nerve.” Three characters, three missing qualities, one ingeniously reusable compositional device.
| Fun Facts — The Song | |
|---|---|
| The Irony | The Scarecrow is demonstrably the cleverest character in the film. He devises the plan to rescue Dorothy, keeps calm when others panic, and solves the group’s problems throughout. He already has the brain he longs for — the Wizard just makes it official with a diploma. |
| The Melody | Arlen’s tune is built on a simple, bouncy pentatonic phrase that recurs throughout the score — it reappears in “We’re Off to See the Wizard” and in underscore cues. Its singability is exactly why it survived eighty-five years of parody, cover, and classroom use. |
| Covers | Versions exist from Diana Ross in The Wiz (1978), Toto (on Toto IV, 1982), They Might Be Giants, Erasure, and dozens of jazz and novelty recordings. The song’s structure — a repeated “if” clause building to a punchline — is a songwriter’s template. |
| Ray Bolger | Bolger wore a latex rubber face mask (created by Jack Dawn) so anatomically convincing it reportedly left permanent creases on his skin after months of filming. His rubber-legged dance style became one of the most imitated physical performances in Hollywood history. |
| Parody-Ready | The song’s premise — a character confidently describing something they “only” lack — is structurally perfect for substitution. TNT’s “If I Only Had a Vertex” (1997) is one of thousands of academic, comedic, and political parodies this template has produced. |
About the film — The Wizard of Oz (MGM, 1939)
The Wizard of Oz opened at the Capitol Theatre in New York on August 15, 1939, and received its national release on August 25. Directed primarily by Victor Fleming (with uncredited contributions from Richard Thorpe and King Vidor), it adapted L. Frank Baum’s 1900 novel The Wonderful Wizard of Oz. Judy Garland was sixteen when filming began in 1938.
| Fun Facts — The Film | |
|---|---|
| Budget | Approximately $2.777 million — enormous for 1939. Over 600 crew members and thousands of extras, including 124 adult actors of short stature as the Munchkins. |
| Technicolor | The shift from sepia-toned Kansas to full three-strip Technicolor Oz is one of cinema’s most calculated reveals. Using sepia first was a deliberate storytelling choice, not a technical constraint. |
| Ruby Slippers | In Baum’s novel the slippers were silver. MGM changed them to ruby red to show off Technicolor. A production pair sold at auction in 2023 for $32.5 million — arguably the most famous prop in film history. |
| Academy Awards | Won two Oscars: Best Original Score (Herbert Stothart) and Best Original Song for “Over the Rainbow.” That song was nearly cut from the final edit; studio executives felt it slowed the opening. |
| Box Office | The film barely broke even in its original 1939 theatrical run. It became a classic through annual CBS television broadcasts beginning in 1956 — a reminder that initial reception is not destiny. |
| Margaret Hamilton | The actress playing the Wicked Witch wore copper-based green face paint that was mildly toxic. A pyrotechnic stunt during the Munchkinland scene burned her seriously and required six weeks of recovery. |
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“If I Only Had a Brain” — Ray Bolger as the Scarecrow, The Wizard of Oz (1939)
Dorothy meets the Scarecrow on the Yellow Brick Road and he introduces himself with the song. Notice the premise: a character implying a deficit he demonstrably does not have. He will outthink everyone for the rest of the film.