Find the X and Y Intercepts y=4x^2-9x+5

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Algebra

$y = 4 x^{2} - 9 x + 5$

Find the x-intercepts.

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To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = 4 x^{2} - 9 x + 5$

Solve the equation.

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Rewrite the equation as $4 x^{2} - 9 x + 5 = 0$ .

$4 x^{2} - 9 x + 5 = 0$

Factor by grouping.

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For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot 5 = 20$ and whose sum is $b = - 9$ .

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Factor $- 9$ out of $- 9 x$ .

$4 x^{2} - 9 x + 5 = 0$

Rewrite $- 9$ as $- 4$ plus $- 5$

$4 x^{2} + (- 4 - 5) x + 5 = 0$

Apply the distributive property.

$4 x^{2} - 4 x - 5 x + 5 = 0$

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

$(4 x^{2} - 4 x) - 5 x + 5 = 0$

Factor out the greatest common factor (GCF) from each group.

$4 x (x - 1) - 5 (x - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $x - 1$ .

$(x - 1) (4 x - 5) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 1 = 0$

$4 x - 5 = 0$

Set the first factor equal to $0$ and solve.

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Set the first factor equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Set the next factor equal to $0$ and solve.

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Set the next factor equal to $0$ .

$4 x - 5 = 0$

Add $5$ to both sides of the equation.

$4 x = 5$

Divide each term by $4$ and simplify.

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Divide each term in $4 x = 5$ by $4$ .

$\frac{4 x}{4} = \frac{5}{4}$

Cancel the common factor of $4$ .

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Cancel the common factor.

$\frac{4 x}{4} = \frac{5}{4}$

Divide $x$ by $1$ .

$x = \frac{5}{4}$

The final solution is all the values that make $(x - 1) (4 x - 5) = 0$ true.

$x = 1, \frac{5}{4}$

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (\frac{5}{4}, 0)$

Find the y-intercepts.

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To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = 4 {(0)}^{2} - 9 \cdot 0 + 5$

Solve the equation.

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Remove parentheses.

$y = 4 {(0)}^{2} - 9 \cdot 0 + 5$

Simplify $4 {(0)}^{2} - 9 \cdot 0 + 5$ .

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Simplify each term.

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Raising $0$ to any positive power yields $0$ .

$y = 4 \cdot 0 - 9 \cdot 0 + 5$

Multiply $4$ by $0$ .

$y = 0 - 9 \cdot 0 + 5$

Multiply $- 9$ by $0$ .

$y = 0 + 0 + 5$

Simplify by adding zeros.

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Add $0$ and $0$ .

$y = 0 + 5$

Add $0$ and $5$ .

$y = 5$

y-intercept(s) in point form.

y-intercept(s): $(0, 5)$

List the intersections.

x-intercept(s): $(1, 0), (\frac{5}{4}, 0)$

y-intercept(s): $(0, 5)$

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